In the stream 8 1 4 7 2 0 5, how many successes occurred?

Answer: 3 Successes are digits 0, 1, 2: the digits 1, 2, 0 = 3 successes.

Simulating an experiment many times and computing the relative frequency estimates

Answer: The probability empirically (more accurate as repetitions increase) Simulation gives Monte Carlo estimates of probabilities.

The Law of Large Numbers says

Answer: Sample mean approaches population mean as n grows LLN: x̄ → μ as n → ∞.

AP Statistics · Topic 4.2

Estimating Probabilities Using Simulation Practice

Part of Probability, Random Variables, and Probability Distributions.(UNC-2.A)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$To simulate an event with probability 0.3, digits 0, 1, 2 represent success.$
$In the stream 8 1 4 7 2 0 5, how many successes occurred?$
- A
  $4$
- B
  $1$
- C
  $2$
- D
  $3$
  check_circle
Why
$Successes are digits 0, 1, 2: the digits 1, 2, 0 = 3 successes.$
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Sample 2difficulty 3/5
$Simulating an experiment many times and computing the relative frequency estimates$
- A
  $The variance of the population$
- B
  $The probability empirically (more accurate as repetitions increase)$
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- C
  $Nothing useful$
- D
  $The exact probability$
Why
$Simulation gives Monte Carlo estimates of probabilities.$
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Sample 3difficulty 3/5
$The Law of Large Numbers says$
- A
  $Mean = SD$
- B
  $Sample mean approaches population mean as n grows$
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- C
  $Probability changes with each trial$
- D
  $Sample size shrinks$
Why
$LLN: x̄ \to μ as n \to \infty.$
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Sample 4difficulty 3/5
$To simulate a 30% probability event using a random number generator producing values 0-99.$
$Which assignment is correct?$
- A
  $1-30 = success, 31-100 = failure$
- B
  $0-3 = success$
- C
  $0-29 = success, 30-99 = failure$
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- D
  $0-30 = success$
Why
$30 outcomes (0-29) out of 100 represent the 30% probability of success.$
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Sample 5difficulty 3/5
$Running 10,000 simulations and getting 4,328 "successes" estimates p as$
- A
  $0.5$
- B
  $0.4328$
  check_circle
- C
  $1/10000$
- D
  $4328$
Why
$Estimate = number of successes / number of trials.$
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